AN INTERPRETATION THEORY FOR INDUCED POLARIZATION VERTICAL SOUNDINGS (TIME-DOMAIN)*

In this paper it is shown how one may obtain a generalized Ohm's law which relates the induced polarization electric field to the steady-state current density through the introduction of a fictitious resistivity defined as the product of the chargeability and the resistivity of a given medium. The potential generated by the induced polarization is calculated at any point in a layered earth by the same procedure as used for calculating the potential due to a point source of direct current. On the basis of the definition of the apparent chargeability m_a, the expressions of m_a for different stratigraphie situations are obtained, provided the IP measurements are carried out on surface with an appropriate AMNB array. These expressions may be used to plot master curves for IP vertical soundings. Finally some field experiments over sedimentary formations and the quantitative interpretation procedure are reported.     

A NEW PARAMETER FOR THE INTERPRETATION OF INDUCED POLARIZATION FIELD PROSPECTING (time-domain) *

In a previous paper it has been shown that we can relate the transient IP electric field E_p , existing in a rock after a step wave of polarizing current, with the steady-state current density J_ss during the current step wave as follows: E_p =ρ' J_ss . This relation may be interpreted as a generalized Ohm's law, valid in linear cases, in which ρ’(fictitious resistivity) is defined as the product of the true resistivity ρ with the chargeability m. Supposing E _p=— grad U_p and applying the divergence condition div J_ss = o, one can, for a layered earth, obtain a general expression for the depolarization potential U_p as a solution of Laplace's equation ?²U_p= o. Since the mathematical procedure for the solution of this last equation is identical to that used in resistivity problems, we propose now the introduction of an apparent fictitious resistivity ρ'_a (defined as the product of the apparent resistivity ρ_a with the apparent chargeability m_a) as a new parameter for the interpretations of IP soundings carried out over layered structures with a common electrode array. The most general expression of ρ'_a as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'_a. Therefore it is possible to interpret a ρ'_a field curve using the same standard graphs for resistivity prospecting with the usual method of complete curve matching. In this manner a great deal of work is saved since there is no need to construct proper m_a graphs for the interpretation of IP soundings, as it has been done up to now. Finally some field examples are reported.     

Inversion of 2D spectral induced polarization imaging data

Laboratory measurements of various materials suggest that more information can be obtained by measuring the in‐phase and out‐of‐phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole‐Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced‐polarization (IP) surveys, the Cole‐Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole‐Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole‐Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non‐homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least‐squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.     

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.     

EXAMPLES OF RESOLUTION IMPROVEMENT IN GEOELECTRICAL SOUNDINGS APPLIED TO GROUNDWATER INVESTIGATIONS1

One simulation and two field examples from New Jersey illustrate resolution improvement in geoelectrical soundings applied to groundwater exploration. Layered-earth parameter resolution is derived from data obtained with the commonly used methods of resistivity, induced polarization (IP) and transient electromagnetic (TEM) soundings. Resolution improvement is achieved by simultaneous inversion of two or more data sets and by constraining parameters of the inverse problem. A quantitative analysis showing the contribution of IP data to the resolution of geo-electric sections is presented. Simultaneous inversion of simple IP data with conventional resistivity and resistivity-TEM data sets resulted in improved parameter resolution. IP data improved resolution in three ways: (1) by decoupling correlated layered-earth parameters, (2) by adding information to a geological interpretation about a second physical property, namely chargeability, and (3) by increasing the electrical information available.     

Study of the Santa Catarina aquifer system (Mexico Basin) using magnetotelluric soundings

A tensor magnetotelluric test survey was carried out in the region of Santa Catarina, located in the Chalco sub-basin of the Mexico Basin. The objective was to define the stratification at depth with an emphasis on the geometry of the main aquifer of that region which is partially known from DC resistivity soundings and drilling. High-quality magnetotelluric soundings could be recorded in the immediate vicinity of large urban zones because the sub-surface is very conductive. Interpretation shows that the solid bedrock is located at a depth of at least 800 m to the south and 1300 m to the north; it could, however, be much deeper. Using complementary DC resistivity sounding and well-logging data, three main layers have been defined overlying the bedrock. These layers are, from surface to bottom, an unsaturated zone of sand, volcanic ash and clay about 10 m thick, followed by a very conductive (1.5 ohm·m) 200 m thick layer of sand and ash with intercalated clay, saturated with highly mineralized water, and finally a zone with resistivity increasing gradually to 60 ohm·m. The investigated deep aquifer constitutes most of this third layer. It consists of a sequence of sand, gravel, pyroclastites and mainly fractured basalts. MT resistivity soundings and magnetic transfer functions also indicate that a shallow resistive structure is dipping, from the northwest, into the lacustrine deposits of the basin. This geologic feature is likely to be highly permeable fractured basaltic flows, which provide a channel by which water contaminated by the Santa Catarina landfill may leak into the basin.     

RELATIONS OF IP DECAY-CURVE STATISTICS AND GEOLOGY*

Six thousand three hundred IP measurements made in central and southern Germany have been statistically evaluated. Shapes of IP decay curves obtained in the course of routine prospecting for sulfides were characterized in the following way: three chargeabilities were recorded during the 2 s current-off time. By dividing the last by the first chargeability an “IP decay coefficient’ was calculated and statistically evaluated by means of histograms. When the histograms were compared with the statistics of apparent resistivity and chargeability, no relationship could be detected. Therefore, the histograms of M3/M1 values represent a characteristic property of distinct areas with certain geological features, mineral assemblage and tectonics. Weathering does not alter this geophysical “fingerprint”, which depends solely on geology.     

AN APPROACH TO THE IDENTIFICATION OF FINE SEDIMENTS BY INDUCED POLARIZATION LABORATORY MEASUREMENTS*

Time-domain-induced polarization (IP) laboratory measurements were performed on about 200 fine sediment samples with varying water content. The results permitted an analysis of IP properties of clays, loams, silts, and sands. Particular emphasis has been given to the analysis of the chargeability m as a function of lithotype and the water content. By analyzing decay curves, a new parameter was identified. It is a statistically specific characteristic of the lithotype and is independent of the water content. Therefore, it provides a diagnostic parameter for lithotype identification. In association with the values of chargeability and electrical resistivity, this parameter permits a reliable evaluation of water content and yields useful information about the porosity and permeability of the lithotype.     

Localization and characterization of cracks in clay‐rocks using frequency and time‐domain induced polarization

Induced polarization (IP) is a geophysical method that is potentially sensitive to the presence of cracks in porous rocks and therefore to damage. We performed time‐domain and frequency domain IP measurements at the Tournemire Underground Research Laboratory (URL, Aveyron, France) in areas where different types of cracks are observed. These cracks correspond to both tectonic fractures and new cracks associated with stress release and desiccation resulting from the excavation of a gallery. These measurements were performed both in eastern and northern galleries of the test site. The eastern gallery was excavated in 1996 while the northern gallery was excavated recently in 2008. This gives us the opportunity to study the electrical characteristics of the excavation damaged zone surrounding the galleries with respect to the age of the excavation. Longitudinal profiles were performed along the floor of the galleries with 48 Cu/CuSO₄ electrodes separated by a distance of 20 cm. Chargeability and resistivity were inverted using a Gauss‐Newton iterative approach assuming an isotropic heterogeneous clay‐rock material. The resulting IP tomograms show a correlation between high values of chargeability and the presence of calcite‐filled tectonic fractures. X‐ray analysis indicates that the presence of pyrite in these fractures is a potential source of the observed IP signals. The cracks associated with the mechanical damage of the formation exhibit low values of chargeability, on the same order of magnitude than the chargeability of the clay‐rock matrix and are therefore hardly observable. A smaller IP response associated with the presence of these cracks is observed in the older gallery and this observation is qualitatively related to the desaturation process associated with these cracks. In a specific area of one of the galleries, the presence of calcareous nodules is observed to be an important source of anomalous chargeability. This signature seems to be associated with the presence of pyrite.     

A SIMPLE DERIVATION OF SEIGEL'S TIME DOMAIN INDUCED POLARIZATION FORMULA *

It is advantageous to postulate the phenomenological equivalence of chargeability with a slight increase in resistivities rather than a similar reduction in the conductivities. Substitution of these increments in the expression for the total differential of apparent resistivity leads directly to Seigel's formula. Included also are (i) an equally simple demonstration that, for a homogeneously chargeable ground with arbitrary resistivity distribution, the apparent chargeability m_a, equals the true homogeneous value m, and (ii) a direct derivation of the completely general resistivity relation where the symbols have the usual meanings.     

AN ELECTRICAL RESISTIVITY PROFILE IN HAWAII WITH NOVEL ELEVATION CORRECTION*

In order to locate relatively optimum sites for drilling exploratory holes for fresh water, an electrical resistivity survey was conducted along the new Mahukona-Kawaihae Road on the west flank of the Kohala Mountain. Two resistivity soundings made at the same stations, using the Schlumberger electrode configuration, determined an a spacing of 275 feet for horizontal profiling with the Wenner array. The correlation coefficient of the elevation to profile data was 0.41. A procedure for removing elevation effect from observed apparent resistivity was developed. Based on the reduced resistivity profile, four relatively optimum sites for additional exploration, such as by drilling, are specified. There is no specific interpretation of the data that can definitely indicate the occurrence of large underground reservoirs of fresh water anywhere along the profile. This is because the interpretation of horizontal profiling data is essentially relative and not absolute.     

Assessment of aquifer vulnerability to industrial waste water using resistivity measurements. A case study, along El-Gharbyia main drain, Nile Delta, Egypt

1D resistivity sounding and 2D resistivity imaging surveys were integrated with geological and hydrochemical data to assess the aquifer vulnerability and saltwater intrusion in the north of Nile Delta, Egypt. In the present study, the El-Gharbyia main drain was considered as a case study to map the sand bodies within the upper silt and clay aquitard. Twenty Schlumberger soundings and six 2D dipole-dipole profiles were executed along one profile close to the western side of the main drain. In addition, 14 groundwater samples and 4 surface water samples from the main drain were chemically analyzed to obtain the major and trace elements concentrations.The results from the resistivity and hydrochemical data were used to assess the protection of the groundwater aquifer and the potential risk of groundwater pollution. The inverted resistivities and thicknesses of the layers above the aquifer layer were used to estimate the integrated electrical conductivity (IEC) that can be used for quantification of aquifer vulnerability. According to the aquifer vulnerability assessment of an underlying sand aquifer, the southern part of the area is characterized by high vulnerability zone with slightly fresh to brackish groundwater and resistivity values of 11-23 Ω.m below the clay cap. The resistivity sections exhibit some sand bodies within the clay cap that lead to increase the recharging of surface waste water (650 mg/l salinity) and flushing the upper part of underlying saltwater aquifer. The region in the north has saltwater with resistivity less than 6 Ω.m and local vulnerable zones within the clay cap. The inverted 2D dipole-dipole profiles in the vulnerable zones, in combination with drilling information have allowed the identification of subsoil structure around the main drain that is highly affected by waste water.     

Changes in complex resistivity during creep in granite

A sample of Westerly granite was deformed under constant stress conditions: a pore pressure of 5 MPa, a confining pressure of 10 MPa, and an axial load of 170 MPa. Pore volume changes were determined by measuring the volume of pore fluid (0.01M KCl_aq) injected into the sample. After 6 days of creep, characterized by accelerating volumetric stain, the sample failed along a macroscopic fault. Measurements of complex resistivity over the frequency range 0.001–300 Hz, taken at various times during creep, showed a gradual increase in both conductivity and permittivity. When analysed in terms of standard induced polarization (IP) techniques, the changing complex resistivity resulted in systematic changes in such parameters as percent frequency effect and chargeability. These results suggest that it may be possible to monitor the development of dilatancy in the source region of an impending earthquake through standard IP techniques.     

MODEL TANK EXPERIMENTS ON RESOLUTION OF RESISTIVITY ANOMALIES OBTAINED OVER BURIED CONDUCTING DYKES — INLINE AND BROADSIDE PROFILING*

Model tank inline resistivity profiles with Wenner and two-electrode systems obtained over two vertical, parallel, infinitely conducting dykes submerged in water show that the two-electrode resistivity anomalies resolve better than the four-electrodes Wenner. anomalies. In contrast, the broadside resistivity anomalies obtained with a Wenner configuration resolve much better than those obtained with two-electrode configuration over an identical ground structure.     

从瞬变电磁响应中提取IP信息的研究(英文)

在对浙江省某铜矿进行瞬变电磁勘查时,由于感应激发极化效应的影响,造成瞬变电磁晚期测道的数据发生倒转。采用常规的瞬变电磁数据处理方法难以处理,造成晚期测道数据不可用,影响TEM的探测深度及精度。针对这个情况,采用Cole.Cole模型分析了均匀半空问模型中直流电阻率、充电率、时间常数以及频率相关系数对磁性源瞬变电磁响应的影响规律。利用奇异值分解法(The Singular Value Decomposition,简称SVD)对实测TEM数据进行分析及反演,并且从瞬变电磁响应数据中分离出勘探区瞬变电磁测量数据Cole—Cole模型的各参数,将分离出来的参数用于探测结果的辅助解释。经过分析得出充电率和频率相关系数对瞬变电磁响应的影响较大,而直流电阻率和时间常数对其影响较小的结论。通过常规方法和奇异值分解法对实测数据分别进行处理,发现后者视电阻率断面图的异常更加突出,从而较准确的圈定了铜矿体地范围,此结论得到_『钻孔的验证,与实际地质情况吻合较好。     

时间域航空电磁法激电效应对电磁扩散的影响

由于激发极化效应的影响,时间域航空电磁晚期道信号经常会出现变号现象.基于电阻率的传统反演方法无法对变号数据进行正确反演,因此通常在数据处理中予以剔除.为深入了解极化介质的电磁扩散特征,认识航空瞬变电磁负响应的产生机理,本文研究时间域航空电磁系统的电磁扩散特征.我们以均匀极化、非极化半空间及层状介质模型为例,通过直接积分的方法求解频率域电场响应,并由欧姆定律得到电流响应,再经过汉克尔变换得到时间域电流响应.通过研究电流随时间在地下极化介质中的传播特征研究电磁扩散过程;通过对比不同激电参数对电磁扩散的影响,研究极化介质中感应电流与极化电流的扩散规律,从而合理地解释极化介质中负响应的产生机理.基于本文研究和分析结果,可加深对时间域航空电磁法中激电效应的认识.     

A STUDY ON THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDING DATA MEASURED BY WENNER ELECTRODE CONFIGURATION*

This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation where K₁(λ) is the kernel and B₁(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least-squares method. The least-squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions.     

Electrical resistivity characterization and defect detection on a geosynthetic clay liner (GCL) on an experimental site

In this paper we analyze the onsite characterization of a geosynthetic clay liner (GCL) that serves to ensure the impermeability of a landfill cap by DC electrical methods. The imaging of the GCL geoelectrical properties is a challenging problem because it is a very thin (between 4 and 7 mm thick) and resistive layer (from 100,000 to 2,000,000 Ω·m) depending on meteorological conditions and aging. We compare results obtained using electrical resistivity tomography (ERT) using two different kinds of arrays (dipole–dipole DD and Wenner–Schlumberger) on an experimental site with engineered defects. To confirm these results and to find the real onsite GCL resistivity we have performed sampling of the posterior distribution of this parameter using vertical electrical sounding (VES) inversions. Different VES methods were extracted from ERT with DD array and converted into a Schlumberger array.As a main conclusion the dipole–dipole array provides a better resistivity resolution of the defects than the Wenner–Schlumberger array. On ERT images, the defect detection seems to be impossible if the GCL has very high resistivity, as it happened when it was put in place. Taking into account the equivalence rules, the inversions are in both cases (ERT and VES) compatible. The GCL resistivity estimated from PSO (particle swarm optimization) varies from 3.0 10⁵ to 1.10⁶ Ω·m depending on saturation conditions during the twenty first months of its placing. Then, the resistivity dropped to 4.10⁴–9.10⁴ Ω·m, indicating a probable chemical damage of the GCL due to aging. Finally the fact that the VES inversions are solved via PSO sampling allows for the detection of a very thin and resistive layer and opens the possibility of performing micro VES surveys along the landfill to detect possible GCL defects.     

THE APPLICATION OF LINEAR FILTER THEORY TO THE DIRECT INTERPRETATION OF GEOELECTRICAL RESISTIVITY SOUNDING MEASUREMENTS*

Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy. In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%.     

RESISTIVITY SOUNDING ON A MULTILAYERED EARTH CONTAINING TRANSITION LAYERS*

For curves over a horizontally stratified earth where any of the layers has a conductivity variation proportional to (1 +β·z)^N, where β and N are arbitrary constants and z is the depth to the layer, expressions for apparent resistivity for Wenner and Schlumberger sounding are derived. No assumption has been made about the continuity of conductivity at the interface. It is shown that most of the previous investigations in this connection can be regarded as particular cases of the present study.